Uniform optimal-order convergence of the LDG method for singularly perturbed problems

主讲人：程瑶 苏州科技大学副教授

时间：2025年4月11日14：00

地点：三号楼332报告厅

举办单位：数理学院

主讲人介绍：程瑶，苏州科技大学信息与计算科学系，副教授，硕导。主要从事奇异摄动问题数值解以及局部间断Galerkin有限元方法的理论和应用研究。主持完成国家自然科学基金青年基金、江苏省自然科学基金、江苏省高校自然科学基金以及校级项目多项。入选江苏高校“青蓝工程”优秀青年骨干教师培养对象。在《Math. Comp.》、《Numer. Math.》和《J. Sci. Comput.》等国内外期刊上发表学术论文三十余篇。

内容介绍：The Local Discontinuous Galerkin (LDG) method is an efficient numerical algorithm for solving singularly perturbed problems whose solutions exhibit boundary layers. In this talk, we present recent convergence results of the LDG method for singularly perturbed convection-reaction-diffusion problems on some typical layer-adapted meshes. We demonstrate optimal-order convergence in the L2-norm, balanced norm, and maximum norm. This is achieved by utilizing several techniques, including energy-norm supercloseness, composite projectors, layer-upwind numerical fluxes, and discrete Green’s functions. Numerical experiments validate our theoretical findings.